A097393 Emirpimes: numbers n such that n and its reversal are distinct semiprimes.

15, 26, 39, 49, 51, 58, 62, 85, 93, 94, 115, 122, 123, 129, 143, 155, 158, 159, 169, 177, 178, 183, 185, 187, 203, 205, 221, 226, 265, 289, 302, 314, 319, 321, 326, 327, 329, 335, 339, 341, 355, 381, 394, 398, 413, 415, 437, 493, 497, 502, 511, 514, 533

Offset: 1

Author

Jonathan Vos Post

Keywords

• nonn
• base

Comments

Computed by Eric W. Weisstein, Aug 13 2004.

Examples

			26 is a semiprime, as it is 2 * 13, and so is 62 = 2 * 31. 26 and 62 are therefore both in the sequence.
		

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 1..10000
• Eric Weisstein's World of Mathematics, Emirpimes

Crossrefs

Cf. A001358, A097394.

Equals A085751 \ A046328.

Programs

Maple

isA097393 := proc(n)
    local R ;
    R := digrev(n) ;
    if R <> n then
        if numtheory[bigomega](R) = 2 and numtheory[bigomega](n) = 2 then
            return true;
        else
            false;
        end if;
      else
        false;
    end if;
end proc:
for n from 1 to 500 do
    if isA097393(n) then
        printf("%d,",n) ;
    end if;
end do: # R. J. Mathar, Apr 05 2012

Mathematica

Cases[{#, IntegerReverse@#} & /@ DeleteCases[Range@5000, ?PalindromeQ], {?(PrimeOmega@# == 2 &) ..}][[All,1]] (* Hans Rudolf Widmer, Jan 07 2024 *)

PARI

rev(n)=subst(Polrev(digits(n)),'x,10)
issemi(n)=bigomega(n)==2
list(lim)=my(v=List(),r);forprime(p=2,lim\2,forprime(q=2,min(lim\p,p),r=rev(p*q);if(issemi(r)&&r!=p*q,listput(v,p*q))));Set(v) \\ Charles R Greathouse IV, Jan 27 2015

Python

from sympy import factorint
from itertools import islice
def sp(n): f = factorint(n); return sum(f[p] for p in f) == 2
def ok(n): r = int(str(n)[::-1]); return r != n and sp(n) and sp(r)
print([k for k in range(534) if ok(k)]) # Michael S. Branicky, Jul 03 2022